cp-algo/structures/fenwick_set.hpp

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• Last update: 2025-05-31 15:49:41+02:00
• Include: #include "cp-algo/structures/fenwick_set.hpp"

Depends on

• cp-algo/structures/bit_array.hpp
• cp-algo/structures/fenwick.hpp
• cp-algo/util/bit.hpp
• cp-algo/util/simd.hpp

Verified with

• Ordered Set (verify/structures/fenwick/ordered_set.test.cpp)

Code

#ifndef CP_ALGO_STRUCTURES_FENWICK_SET_HPP
#define CP_ALGO_STRUCTURES_FENWICK_SET_HPP
#include "fenwick.hpp"
#include "bit_array.hpp"
namespace cp_algo::structures {
    template<size_t maxc>
    using popcount_array = std::array<int, maxc / bit_width<uint64_t> + 1>;
    // fenwick-based set for [0, maxc)
    template<size_t maxc>
    struct fenwick_set: fenwick<int, popcount_array<maxc>> {
        using Base = fenwick<int, popcount_array<maxc>>;
        static constexpr size_t word = bit_width<uint64_t>;
        size_t sz = 0;
        bit_array<maxc> bits;

        fenwick_set(): Base(popcount_array<maxc>{}) {}
        fenwick_set(auto &&range): fenwick_set() {
            for(auto x: range) {
                Base::data[x / word + 1] += 1;
                if(!bits.test(x)) {
                    sz++;
                    bits.flip(x);
                }
            }
            Base::to_prefix_folds();
        }
        void insert(size_t x) {
            if(bits.test(x)) return;
            Base::update(x / word, 1);
            bits.flip(x);
            sz++;
        }
        void erase(size_t x) {
            if(!bits.test(x)) return;
            Base::update(x / word, -1);
            bits.flip(x);
            sz--;
        }
        size_t order_of_key(size_t x) const {
            return Base::prefix_fold(x / word) + order_of_bit(bits.word(x / word), x % word);
        }
        size_t find_by_order(size_t order) const {
            if(order >= sz) {
                return -1;
            }
            auto [x, pref] = Base::prefix_lower_bound((int)order);
            return x * word + kth_set_bit(bits.word(x), order - pref);
        }
        size_t lower_bound(size_t x) const {
            if(bits.test(x)) {return x;}
            auto order = order_of_key(x);
            return order < sz ? find_by_order(order) : -1;
        }
        size_t pre_upper_bound(size_t x) const {
            if(bits.test(x)) {return x;}
            auto order = order_of_key(x);
            return order ? find_by_order(order - 1) : -1;
        }
    };
}
#endif // CP_ALGO_STRUCTURES_FENWICK_SET_HPP

#line 1 "cp-algo/structures/fenwick_set.hpp"


#line 1 "cp-algo/structures/fenwick.hpp"


#include <cassert>
#include <vector>
namespace cp_algo::structures {
    template <typename Op>
    struct inverse_op {};

    template <typename T>
    struct inverse_op<std::plus<T>> {
        static T apply(T const& a, T const& b) {
            return a - b;
        }
    };

    template <typename T>
    struct inverse_op<std::multiplies<T>> {
        static T apply(T const& a, T const& b) {
            return a / b;
        }
    };

    template<typename T, std::ranges::range Container = std::vector<T>, typename Op = std::plus<T>>
    struct fenwick {
        Op op;
        size_t n;
        Container data;

        fenwick(auto &&range, Op &&op = Op{}): op(std::move(op)) {
            assign(std::move(range));
        }
        void to_prefix_folds() {
            for(size_t i = 1; i < n; i++) {
                if(i + (i & -i) <= n) {
                    data[i + (i & -i)] = op(data[i + (i & -i)], data[i]);
                }
            }
        }
        void assign(auto &&range) {
            n = size(range) - 1;
            data = std::move(range);
            to_prefix_folds();
        }
        void update(size_t x, T const& v) {
            for(++x; x <= n; x += x & -x) {
                data[x] = op(data[x], v);
            }
        }
        // fold of [0, r)
        T prefix_fold(size_t r) const {
            assert(r <= n);
            T res = {};
            for(; r; r -= r & -r) {
                res = op(res, data[r]);
            }
            return res;
        }
        // fold of [l, r)
        T range_fold(size_t l, size_t r) const {
            return inverse_op<Op>::apply(prefix_fold(r), prefix_fold(l));
        }
        // Last x s.t. prefix_fold(x) <= k
        // Assumes prefix_fold is monotonic
        // returns [x, prefix_fold(x)]
        auto prefix_lower_bound(T k) const {
            size_t x = 0;
            T pref = {};
            for(size_t i = std::bit_floor(n); i; i /= 2) {
                if(x + i <= n && op(pref, data[x + i]) <= k) {
                    pref = op(pref, data[x + i]);
                    x += i;
                }
            }
            return std::pair{x, pref};
        }
    };

    template<std::ranges::range Container, typename Op>
    fenwick(Container&&, Op&&) -> fenwick<std::ranges::range_value_t<Container>, Container, Op>;
    template<std::ranges::range Container>
    fenwick(Container&&) -> fenwick<std::ranges::range_value_t<Container>, Container>;

    auto maxer = [](auto const& a, auto const& b) {
        return std::max(a, b);
    };
    template<typename T, std::ranges::range Container = std::vector<T>>
    struct fenwick_max: fenwick<T, Container, decltype(maxer)> {
        using fenwick<T, Container, decltype(maxer)>::fenwick;
    };
    template<std::ranges::range Container>
    fenwick_max(Container&&) -> fenwick_max<std::ranges::range_value_t<Container>, Container>;

}

#line 1 "cp-algo/structures/bit_array.hpp"


#line 1 "cp-algo/util/bit.hpp"


#line 1 "cp-algo/util/simd.hpp"


#include <experimental/simd>
#include <cstdint>
#include <cstddef>
#include <memory>
namespace cp_algo {
    template<typename T, size_t len>
    using simd [[gnu::vector_size(len * sizeof(T))]] = T;
    using i64x4 = simd<int64_t, 4>;
    using u64x4 = simd<uint64_t, 4>;
    using u32x8 = simd<uint32_t, 8>;
    using i32x4 = simd<int32_t, 4>;
    using u32x4 = simd<uint32_t, 4>;
    using i16x4 = simd<int16_t, 4>;
    using u8x32 = simd<uint8_t, 32>;
    using dx4 = simd<double, 4>;

    [[gnu::target("avx2")]] inline dx4 abs(dx4 a) {
    return a < 0 ? -a : a;
    }

    // https://stackoverflow.com/a/77376595
    // works for ints in (-2^51, 2^51)
    static constexpr dx4 magic = dx4() + (3ULL << 51);
    [[gnu::target("avx2")]] inline i64x4 lround(dx4 x) {
        return i64x4(x + magic) - i64x4(magic);
    }
    [[gnu::target("avx2")]] inline dx4 to_double(i64x4 x) {
        return dx4(x + i64x4(magic)) - magic;
    }

    [[gnu::target("avx2")]] inline dx4 round(dx4 a) {
        return dx4{
            std::nearbyint(a[0]),
            std::nearbyint(a[1]),
            std::nearbyint(a[2]),
            std::nearbyint(a[3])
        };
    }

    [[gnu::target("avx2")]] inline u64x4 low32(u64x4 x) {
        return x & uint32_t(-1);
    }
    [[gnu::target("avx2")]] inline auto swap_bytes(auto x) {
        return decltype(x)(__builtin_shufflevector(u32x8(x), u32x8(x), 1, 0, 3, 2, 5, 4, 7, 6));
    }
    [[gnu::target("avx2")]] inline u64x4 montgomery_reduce(u64x4 x, uint32_t mod, uint32_t imod) {
        auto x_ninv = u64x4(_mm256_mul_epu32(__m256i(x), __m256i() + imod));
        x += u64x4(_mm256_mul_epu32(__m256i(x_ninv), __m256i() + mod));
        return swap_bytes(x);
    }

    [[gnu::target("avx2")]] inline u64x4 montgomery_mul(u64x4 x, u64x4 y, uint32_t mod, uint32_t imod) {
        return montgomery_reduce(u64x4(_mm256_mul_epu32(__m256i(x), __m256i(y))), mod, imod);
    }
    [[gnu::target("avx2")]] inline u32x8 montgomery_mul(u32x8 x, u32x8 y, uint32_t mod, uint32_t imod) {
        return u32x8(montgomery_mul(u64x4(x), u64x4(y), mod, imod)) |
               u32x8(swap_bytes(montgomery_mul(u64x4(swap_bytes(x)), u64x4(swap_bytes(y)), mod, imod)));
    }
    [[gnu::target("avx2")]] inline dx4 rotate_right(dx4 x) {
        static constexpr u64x4 shuffler = {3, 0, 1, 2};
        return __builtin_shuffle(x, shuffler);
    }

    template<std::size_t Align = 32>
    [[gnu::target("avx2")]] inline bool is_aligned(const auto* p) noexcept {
        return (reinterpret_cast<std::uintptr_t>(p) % Align) == 0;
    }

    template<class Target>
    [[gnu::target("avx2")]] inline Target& vector_cast(auto &&p) {
        return *reinterpret_cast<Target*>(std::assume_aligned<alignof(Target)>(&p));
    }
}

#line 5 "cp-algo/util/bit.hpp"
#include <array>
#include <bit>
namespace cp_algo {
    template<typename Uint>
    constexpr size_t bit_width = sizeof(Uint) * 8;

    // n < 64
    uint64_t mask(size_t n) {
        return (1ULL << n) - 1;
    }
    size_t order_of_bit(auto x, size_t k) {
        return k ? std::popcount(x << (bit_width<decltype(x)> - k)) : 0;
    }
    [[gnu::target("bmi2")]] inline size_t kth_set_bit(uint64_t x, size_t k) {
        return std::countr_zero(_pdep_u64(1ULL << k, x));
    }
    template<int fl = 0>
    void with_bit_floor(size_t n, auto &&callback) {
        if constexpr (fl >= 63) {
            return;
        } else if (n >> (fl + 1)) {
            with_bit_floor<fl + 1>(n, callback);
        } else {
            callback.template operator()<1ULL << fl>();
        }
    }
    void with_bit_ceil(size_t n, auto &&callback) {
        with_bit_floor(n, [&]<size_t N>() {
            if(N == n) {
                callback.template operator()<N>();
            } else {
                callback.template operator()<N << 1>();
            }
        });
    }

    [[gnu::target("avx2")]] inline uint32_t read_bits(char const* p) {
        return _mm256_movemask_epi8(__m256i(vector_cast<u8x32 const>(p[0]) + (127 - '0')));
    }
    [[gnu::target("avx2")]] inline uint64_t read_bits64(char const* p) {
        return read_bits(p) | (uint64_t(read_bits(p + 32)) << 32);
    }

    [[gnu::target("avx2")]] inline void write_bits(char *p, uint32_t bits) {
        static constexpr u8x32 shuffler = {
            0, 0, 0, 0, 0, 0, 0, 0,
            1, 1, 1, 1, 1, 1, 1, 1,
            2, 2, 2, 2, 2, 2, 2, 2,
            3, 3, 3, 3, 3, 3, 3, 3
        };
        auto shuffled = u8x32(_mm256_shuffle_epi8(__m256i() + bits, __m256i(shuffler)));
        static constexpr u8x32 mask = {
            1, 2, 4, 8, 16, 32, 64, 128,
            1, 2, 4, 8, 16, 32, 64, 128,
            1, 2, 4, 8, 16, 32, 64, 128,
            1, 2, 4, 8, 16, 32, 64, 128
        };
        for(int z = 0; z < 32; z++) {
            p[z] = shuffled[z] & mask[z] ? '1' : '0';
        }
    }
    [[gnu::target("avx2")]] inline void write_bits64(char *p, uint64_t bits) {
        write_bits(p, uint32_t(bits));
        write_bits(p + 32, uint32_t(bits >> 32));
    }
}

#line 5 "cp-algo/structures/bit_array.hpp"
namespace cp_algo::structures {
    template<typename C>
    concept Resizable = requires(C& c, std::size_t n) { c.resize(n); };

    template<class Cont>
    struct _bit_array {
        static constexpr size_t width = bit_width<uint64_t>;
        size_t words, n;
        alignas(32) Cont data;

        constexpr void resize(size_t N) {
            n = N;
            words = (n + width - 1) / width;
            if constexpr (Resizable<Cont>) {
                data.resize(words);
            } else {
                assert(std::size(data) >= words);
            }
        }

        constexpr _bit_array(): n(0), words(0), data() {}
        constexpr _bit_array(size_t N): data() {
            resize(N);
        }

        constexpr uint64_t& word(size_t x) {
            return data[x];
        }
        constexpr uint64_t word(size_t x) const {
            return data[x];
        }
        constexpr void set_all(uint64_t val = -1) {
            for(auto& w: data) {w = val;}
        }
        constexpr void reset() {
            set_all(0);
        }
        constexpr void set(size_t x) {
            word(x / width) |= 1ULL << (x % width);
        }
        constexpr void reset(size_t x) {
            word(x / width) &= ~(1ULL << (x % width));
        }
        constexpr void flip(size_t x) {
            word(x / width) ^= 1ULL << (x % width);
        }
        constexpr bool test(size_t x) const {
            return (word(x / width) >> (x % width)) & 1;
        }
        constexpr bool operator[](size_t x) const {
            return test(x);
        }
        constexpr size_t size() const {
            return n;
        }
    };

    template<size_t N>
    struct bit_array: _bit_array<std::array<uint64_t, (N + 63) / 64>> {
        using Base = _bit_array<std::array<uint64_t, (N + 63) / 64>>;
        using Base::Base, Base::words, Base::data;
        constexpr bit_array(): Base(N) {}
    };
    struct dynamic_bit_array: _bit_array<std::vector<uint64_t>> {
        using Base = _bit_array<std::vector<uint64_t>>;
        using Base::Base, Base::words;
        constexpr dynamic_bit_array(size_t N): Base(N) {
            data.resize(words);
        }
    };

}

#line 5 "cp-algo/structures/fenwick_set.hpp"
namespace cp_algo::structures {
    template<size_t maxc>
    using popcount_array = std::array<int, maxc / bit_width<uint64_t> + 1>;
    // fenwick-based set for [0, maxc)
    template<size_t maxc>
    struct fenwick_set: fenwick<int, popcount_array<maxc>> {
        using Base = fenwick<int, popcount_array<maxc>>;
        static constexpr size_t word = bit_width<uint64_t>;
        size_t sz = 0;
        bit_array<maxc> bits;

        fenwick_set(): Base(popcount_array<maxc>{}) {}
        fenwick_set(auto &&range): fenwick_set() {
            for(auto x: range) {
                Base::data[x / word + 1] += 1;
                if(!bits.test(x)) {
                    sz++;
                    bits.flip(x);
                }
            }
            Base::to_prefix_folds();
        }
        void insert(size_t x) {
            if(bits.test(x)) return;
            Base::update(x / word, 1);
            bits.flip(x);
            sz++;
        }
        void erase(size_t x) {
            if(!bits.test(x)) return;
            Base::update(x / word, -1);
            bits.flip(x);
            sz--;
        }
        size_t order_of_key(size_t x) const {
            return Base::prefix_fold(x / word) + order_of_bit(bits.word(x / word), x % word);
        }
        size_t find_by_order(size_t order) const {
            if(order >= sz) {
                return -1;
            }
            auto [x, pref] = Base::prefix_lower_bound((int)order);
            return x * word + kth_set_bit(bits.word(x), order - pref);
        }
        size_t lower_bound(size_t x) const {
            if(bits.test(x)) {return x;}
            auto order = order_of_key(x);
            return order < sz ? find_by_order(order) : -1;
        }
        size_t pre_upper_bound(size_t x) const {
            if(bits.test(x)) {return x;}
            auto order = order_of_key(x);
            return order ? find_by_order(order - 1) : -1;
        }
    };
}

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